1. Technical Field
The present invention relates to quantum mechanical systems and more particularly to systems and methods that employ principles of quantum mechanics for commodity and legal tender production.
2. Description of the Related Art
Commodities are items for which there is a basic demand and which can be provided through generation processes. Examples are precious metals, such as gold, silver, etc., energy commodities such as oil, gas, and food commodities. In times of massive global devaluation of currencies, commodities offer some potential for preservation of wealth. A reason for this is the difficulty in generating the commodities. This could be, for example, due to mining or due to growing, which also is reflected in the price in terms of fiat currencies that have to be paid according to the market value of the commodity.
A basic problem with commodities that have money-like features, e.g., precious metals, is that they can become subject to speculation (“cornering the market”, sell/buy transactions without underlying physical assets, manipulation in futures markets, etc.). They can also become extremely scarce as some governments or private entities buy them on a large scale. One question is whether it is possible to provide substitute commodities in lieu of physical commodities that are based on information only but nevertheless share all the features of real (hard, physical) commodities. Another problem, which is closely related, is whether it is possible to base legal tender, i.e., methods for payment in a monetary system based on fiat currency, e.g., dollar bills, on information only without additional assumptions.
Properties of legal tender and commodities that serve as monetary equivalents should be hard to counterfeit. These items should be easy to verify, and they should be anonymous, leaving no history of previous transactions. For commodities, it is imposed, in addition, that it should be difficult, though not impossible, to generate them, even for a powerful entity such as a government.
Digital cash, as described in D. Chaum, A. Fiat, and M. Naor, “Untraceable electronic cash,” Advances in Cryptology (Crypto'88), Springer Verlag, pp. 319-327, 1990, provides a way for anonymous, untraceable, and transferable implementation of legal tender that is completely electronic. Digital cash security is typically based on computational assumptions, such as the computational hardness of certain problems, and the existence of a trusted third party, such as a central bank or the issuing bank. Most protocols that have been proposed for digital cash suffer from these restrictions as well as the restrictions on off-line payments. Key sizes that are required to implement the schemes are usually quite large, e.g., in the hundreds of megabytes for a single coin.
S. Wiesner, in “Conjugate Coding,” SIGACT News, Vol. 15, No. 1, pp. 78-88, 1983 (hereinafter Wiesner), proposed a quantum cash scheme that uses the fact that quantum state is not cloneable in order to make a “coin” that cannot be duplicated, as it contains a quantum state that is known only to the trusted bank but not to the currency holders. Moreover, the bank is able to use its knowledge in order to verify, given a coin, whether it is authentic or not. The security of Wiesner's construction was unconditional: the coins could not be copied because of the fundamental laws of physics, even if somebody tries to use the most advanced tools in order to produce a counterfeit.
Wiesner's scheme, however, had the disadvantage that only the bank would be able to test the validity of a coin. In order to be verified, a coin had to be sent to the bank, which, of course, made the construction very unpractical. S. Aaronson, in “Quantum copy-protection and quantum money,” IEEE Conference on Computational Complexity, pp. 229-242, 2009 (hereinafter Aaronson), proposed a quantum cash scheme that addressed this drawback of Wiesner by letting each user check the validity of quantum coins. This made the scheme more convenient to use, however, it compromised the unconditional security: the users could not only check, but also forge a coin, if they have enough computational power.
Unfortunately, it can be seen that any scheme that allows any user to check the validity of quantum coins unavoidably also allows them to produce counterfeits, if they have enough computational power.